September 4, 2009

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

1

COMPREHENSIVE ANALYSIS OF SEQUENCE-STRUCTURE
RELATIONSHIPS IN THE LOOP REGIONS OF PROTEINSSHUGO NAKAMURA1
shugo@bi.a.u-tokyo.ac.jp

KENTARO SHIMIZU1
shimizu@bi.a.u-tokyo.ac.jp

1 Department of Biotechnology, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku,

Tokyo 113-8657, Japan
Local sequence-structure relationships in the loop regions of proteins were comprehensively estimated using simple prediction tools based on support vector regression (SVR).
End-to-end distance was selected as a rough structural property of fragments, and theend-to-end distances of an enormous number of loop fragments from a wide variety ofprotein folds were directly predicted from sequence information by using SVR. We foundthat our method was more accurate than random prediction for predicting the structure of fragments comprising 5, 9, and 17 amino acids; moreover, the extended loop
fragments could be successfully distinguished from turn structures on the basis of theirsequences, which implies that the sequence-structure relationships were signiﬁcant forloop fragments with a wide range of end-to-end distances. These results suggest thatmany loop regions as well as helices and strands restrict the conformational space of theentire tertiary structure of proteins to some extent; moreover, our ﬁndings throw lighton the mechanism of protein folding and prediction of the tertiary structure of proteins
without using structural templates.
Keywords: protein; loop; end-to-end distance; prediction; sequence-structure relationship; support vector regression.

1. Introduction
The tertiary structure of a protein is related to its functional properties to a large
extent and is determined by its entire amino acid sequence [3]. The structure ofhelices and strands, which are the major secondary structures of proteins, is related
to their amino acid sequences; hence, their structure can be predicted on the basisof the local amino acid sequence. Recently, it was reported that the prediction
accuracy for 3-state secondary structures (helices, strands, and other structures) is
nearly 80% [1]. While variations in the tertiary structures of helices and strands
are small, the tertiary structures of protein loops that connect helices and strands
are thought to be conformationally ﬂexible and largely aﬀected by the surrounding
residues.
However, researchers have reported that in some cases, local sequences determine local structures, including loop regions. Long-range interactions are essentially important for protein folding, but if local sequences determine local structures to some extent, it leads to restriction of conformational space of the entire

September 4, 2009

2

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

S. Nakamura, & K. Shimizu

tertiary structure, greatly aﬀecting its folding pathway. The sequence-structure relationships for turns in the loop regions have been analyzed [12, 18], and tools forpredicting the existence of turns on the basis of amino acid sequences have beendeveloped [10, 28, 29]. On the basis of clustering of amino acid sequences, Han et al.
analyzed recurring local sequence motifs that cross protein-family boundaries [13].
In addition, they analyzed conservation of secondary and tertiary structures of sequence clusters [14, 15]. Bystroﬀ et al. obtained “I-sites library,” which is a groupof fragments that have similar tertiary structures within sequence clusters [6], andapplied the library to predict the tertiary structure of proteins on the basis of theiramino acid sequences [7]. In several studies, a number of local structural motifs
or the so-called “structural alphabets” were determined by clustering the tertiary
structures of fragments deposited in a protein structure database. The assignmentof these alphabets to a query fragment was predicted using the local amino acidsequences as inputs [4, 9, 17, 25, 30]. The prediction accuracy of loop modelingwithout the use of the structures of regions ﬂanking the loop regions has also beenreported [22].
The abovementioned studies have shown that in certain loop structures, the local sequences and structures are highly related. However, most of these studies usedclustering of sequence and/or structure spaces, and information on fragments thatwere not included in the clusters was neglected. The researchers reported the prediction accuracy for all fragments, including helices and strands; however, very few
of them have reported prediction with comprehensive accuracy for the loop regions.
Moreover, they provided little information on the extent of sequence-structure relationships in loop regions other than the turns, such as the percentage of structuresthat can be predicted on the basis of the sequence information of that region.
In this study, we have comprehensively estimated local sequence-structure relationships in the loop regions of proteins. We estimated the local sequence-structure
relationships by analyzing whether local amino acid sequence information could be
used to determine the structural properties of that region. We did not predict theassignment of structural alphabets. Instead, we directly predicted the structural information of each fragment. We hypothesized that if the accuracy of our prediction
is better than that of random prediction, it implies that local sequences determine
local structures to some extent, and that the sequence-structure relationship canbe detected using our prediction tool. It is expected that the marginal sequencestructure relationships can be detected using rough structural representations. We
adopted end-to-end distance as a rough structural property of fragments. The endto-end distance of protein fragments is one of the parameters that best represent
the structures of fragments [19] and is used for structure prediction [11].
We could have used any prediction tool for our method of prediction, but few local structure prediction tools that were previously reported are available. Therefore,
we developed a simple prediction tool based on support vector regression (SVR).
Our tool was applied to an enormous number of protein fragments comprising 5,
9, and 17 amino acids retrieved from a wide variety of protein folds in the non-

September 4, 2009

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

Sequence-Structure Relationships in Protein Loops
Table 1.
tions.

3

SVR parameters γ and C used for predic-

Fragment length

5

9

17

Input: Amino acids
Input: PSSM

0.1,1.0

0.1,2.0
0.05,5.0

0.05,10.0

redundant structure database, and the prediction accuracy of our tool for the determination of loop structures was compared to the expected accuracy of random
predictions.
2. Materials and Methods
2.1. Preparation of Datasets
We selected fold representative domains from the Structural Classiﬁcation of Proteins (SCOP) 1.71 [5, 23], from which fragments were extracted. Membrane proteinsand protein structures determined by nuclear magnetic resonance (NMR) were excluded. From 702 domain structures, 168,066, 164,703, and 158,704 fragments comprising 5, 9, and 17 amino acids, respectively, were collected; the fragments wereallowed to overlap.
2.2. Predictions Using SVR
To determine the sequence-structure relationships in the loop regions, we used atool for predicting end-to-end distance on the basis of sequence information. Since
few suitable tools that could be applied to an enormous number of fragment dataon a standalone machine and that could allow ﬂexible speciﬁcation of user-deﬁned
inputs were available, we developed a simple prediction tool based on SVR [26].
Epsilon-SVR with radial basis function (RBF) kernel implemented in the LIBSVM 2.83 package [8] was used, and the parameters for SVR — γ for RBF kerneland cost parameter C — were determined by a grid search to obtain the maximum
correlation coeﬃcient of the predicted and actual end-to-end distances (deﬁned as
the distance between Cα atoms of the N-terminal residue and the C-terminal residueof a fragment) on the basis of the 5-fold cross-validation testing described below.
We used the following data as inputs: (1) amino acid sequence (fragments with 9amino acids only) and (2) position-speciﬁc scoring matrix (PSSM). The number ofdimensions of an input vector is 20 × w, where w is the fragment length. PSSMs
were obtained by PSI-BLAST [2] of up to 5 iterations applied to the non-redundant
database (nr) with default parameters; whole-domain sequences were used as queryfragments. The γ and C pairs obtained for predictions are shown in Table 1.
2.3. Calculation of Prediction Accuracy
We estimated the prediction accuracy by using 5-fold cross validation. For 5-foldcross validation, we divided the collected fragment set into 5 subsets. Four subsets

September 4, 2009

4

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

S. Nakamura, & K. Shimizu

0.3

0.25

Loop
All

0.25

Loop
All

0.2

0.2

Probability

Probability

33-Nakamura

0.15

0.15
0.1

0.1
0.05

0.05
0

0
4

6
8
10
12
14
End-to-end distance [angstrom]

16

(a)
0.08

5

10
15
20
25
End-to-end distance [angstrom]

30

(b)
Loop
All

0.07

Probability

0.06
0.05
0.04
0.03
0.02
0.01
0
10

20
30
40
End-to-end distance [angstrom]

50(c)Fig. 1. End-to-end distance distributions for loop structures (“Loop”) and fragments (“All”)
comprising (a) 5, (b) 9, and (c) 17 amino acids.

were used for the training of SVR, and the remaining subset was used for the test.
To eliminate redundancy between the training and test data, we retrieved BLAST
hits for proteins in the test data with an e-value threshold of < 10.0 and a databasesize of 100,000,000, using the proteins in the training data as queries.
Here, we deﬁne a loop fragment as a fragment in which more than half of theconsecutive residues are coil residues (neither helix nor strand residues). For secondary structure assignment, we used DSSP [20]. The structure letters H, G, andI were assigned to helices; B and E were assigned to strands, and other structure
letters were assigned to coils. To eliminate misassignment of beta strands in beta
sheets between protein chains as coils, DSSP was applied to structural data of biological units obtained from the PQS server [16]. The total numbers of loop fragments
were 57,752, 43,450, and 19,385 for fragments comprising 5, 9, and 17 amino acids,
respectively.
Note that the training sets for our prediction include various fragments suchas helices and strands, and not merely the sets of loop fragments. Figure 1(a)–(c)shows the end-to-end distance distributions of fragments comprising 5, 9, and 17
amino acids. The solid lines (“Loop”) show the distributions of loop fragments, andthe dashed lines (“All”) show the distributions of all the fragments. Sharp peaks of
distributions for all the fragments correspond to helices.

September 4, 2009

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

Predicted end-to-end distance [angstrom]

Sequence-Structure Relationships in Protein Loops

5

30
300
250
200
150
100
50
0

25
20
15
10
5
0
0

5

10

15

20

25

30

End-to-end distance [angstrom]Fig. 2. An example of a histogram showing randomly predicted end-to-end distances against theactual end-to-end distances for loop fragments comprising 9 amino acids.

2.4. Random Prediction
The accuracy of random prediction was calculated in order to determine the signiﬁcance of the accuracy of our prediction. As described above, our training sets
included fragments with all kinds of structures such as helices, strands, and loops
with end-to-end distance distributions that were very similar to the “All” lines inFig. 1(a)–(c). Thus, the end-to-end distance for each fragment in the test set was
randomly predicted on the basis of the end-to-end distributions of fragments in the
training sets. A total of 1000 random predictions were made for each set comprisingfragments with 5, 9, and 17 amino acids, and the average correlation coeﬃcientswere calculated to be 0.00015 ± 0.015, −0.00015 ± 0.015, and −0.00022 ± 0.022,
respectively. Figure 2 shows, as an example, the random predictions for fragments
comprising 9 amino acids.

2.5. Dataset from CASP8 Targets
To evaluate the dataset dependency of our results, we applied our prediction tool
to fragments extracted from another set of protein structures. This set belonged
to the “free modeling targets” of the eighth community-wide experiment on the
Critical Assessment of Techniques for Protein Structure Prediction (CASP8) [31].
Free modeling targets were proteins that did not have homologs with known tertiary structures when CASP8 was conducted. We used PSSMs calculated during
the CASP8 prediction term as inputs in SVR. Thus, structural information on thehomologs and the targets themselves, which were made public after CASP8, were
not used for our prediction. From these targets, we extracted 864, 829, and 780
fragments comprising 5, 9, and 17 amino acids, respectively. Among the fragments
comprising 5, 9, and 17 amino acids, 282, 177, and 88, respectively, were loop fragments. We applied our prediction tool to these fragments in the same manner as we
did for the cross-validation testing described above.

September 4, 2009

6

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

S. Nakamura, & K. Shimizu
Table 2. Correlation coeﬃcients between the predicted and actual end–
to-end distances for fragments comprising 5, 9, and 17 amino acids.
Fragment length

Input: Amino acids
Input: PSSM

5

9

17

Loop

All

Loop

All

Loop

All

0.485

0.673

0.313
0.502

0.434
0.666

0.446

0.551

3. Results and Discussion
Table 2 shows the correlation coeﬃcients between the predicted and actual end-toend distances for fragments comprising 5, 9, and 17 amino acids. The values for loop
fragments are given in the “Loop” columns, and those for all the fragments in the“All” columns. In the case of random predictions, i.e., when there is no relationshipbetween the local sequences and local structures, the correlation coeﬃcients should
almost be zero, as described in the random prediction section (2.4) and as shownin Fig. 2.
When amino acid sequence information was used as the input, the correlationcoeﬃcients were above 0.3 for loop fragments and above 0.4 for all the fragments
comprising 9 amino acids; these values are better than those obtained in random
prediction. When PSSM was used as the input, the prediction accuracies signiﬁcantly improved; the correlation coeﬃcients were above 0.4 for the loop fragments
and above 0.5 for all the fragments comprising 5, 9, and 17 amino acids. Previous
researches have reported that for backbone dihedral angle prediction, when PSSM
was used as the input instead of amino acid sequences, the prediction accuracy
improved by only a small extent [21]. We think that we were able to detect theeﬀect of PSSM because we used end-to-end distance, which is a rough structuralproperty, and not backbone dihedral angles, which are very sensitive to the tertiary
structures of fragments.
Figure 3(a)–(c) are histograms showing the predicted and actual end-to-end
distances for loop fragments comprising 5, 9, and 17 amino acids (PSSM input). In
all the cases, there were obvious correlations between the predicted and actual endto-end distance. For 53% of the fragments, the errors in the predicted end-to-end
distances compared to the actual distances were below 20%. In particular, our simple
prediction tool can accurately distinguish fragments with short end-to-end distancesfrom those with long end-to-end distances. When the predicted end-to-end distancewas greater than 20 Å for fragments comprising 9 amino acids, it was found that only
2.5% of them had an actual end-to-end distance of < 10 Å. These results suggestthat the local structures of the extended loops and turns considerably depend on
the local sequences. Figure 3(d) shows the receiver operating characteristic (ROC)
curve for predicting whether the end-to-end distance of a fragment is longer than 20
Å for fragments comprising 9 amino acids. The area under the ROC curve (AUC)
was 0.774, and the maximum Matthews correlation coeﬃcient (MCC) was 0.292;

September 4, 2009

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

16
350
300
250
200
150
100
50
0

14
12
10
8
6
4
2
0
0

2

4

6

8

10

12

14

Predicted end-to-end distance [angstrom]

Predicted end-to-end distance [angstrom]

Sequence-Structure Relationships in Protein Loops

16

30
160
140
120
100
80
60
40
20
0

25
20
15
10
5
0
0

5

End-to-end distance [angstrom]

10

15

20

25

30

End-to-end distance [angstrom]

(a)

(b)
1

50
140
120
100
80
60
40
20
0

40
30
20
10

0.8
Sensitivity

Predicted end-to-end distance [angstrom]

7

0.6
0.4
0.2

0

0
0

10

20

30

40

End-to-end distance [angstrom]

(c)

50

0

0.2

0.4
0.6
0.8
False positive rate

1(d)Fig. 3. Histograms depicting the predicted end-to-end distances against the actual end-to-end
distances for loop fragments comprising (a) 5, (b) 9, and (c) 17 amino acids. (d) Receiver operating
characteristic (ROC) curve for predicting whether the end-to-end distance of a fragment is longer
than 20 Å for fragments comprising 9 amino acids.

these results show that our prediction method is better than random prediction forthe prediction of extended loop structures.
Table 3 shows the correlation coeﬃcients between the predicted and actual endto-end distances for fragments comprising 5, 9, and 17 amino acids extracted fromthe CASP8 dataset. Though the numbers of data are small, the correlation coeﬃcients for these fragments are comparable to those for the fragments in the 5-foldcross-validation test (Table 2), and the results show that the sequence-structure relationships detected by our prediction tool are generally independent of the datasets.
To elucidate the characteristics of amino acid sequences on the basis of theend-to-end distance of loop fragments, we analyzed the amino acid propensity forfragments comprising 9 amino acids. A similar tendency was observed for fragments
comprising 5 and 17 amino acids. We divided the fragments into 4 classes on thebasis of the end-to-end distances: < 10 Å, 10–15 Å, 15–20 Å, and > 20 Å. Subsequently, we calculated the amino acid propensity for fragments of each distance classSeptember 4, 2009

8

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

S. Nakamura, & K. Shimizu
Table 3. Correlation coeﬃcients between the predicted and actual
end-to-end distances for fragments comprising 5, 9, and 17 aminoacids in the CASP8 dataset.
Fragment length

Input: PSSM

123456789
R
K
D
E
N
Q
H
P
Y
W
S
T
G
A
M
C
F
L
V
I

5

-3.0

17

Loop

All

Loop

All

Loop

All

0.472

0.631

0.525

0.625

0.240

0.518

123456789
R
K
D
E
N
Q
H
P
Y
W
S
T
G
A
M
C
F
L
V
I

(a)

9

123456789
R
K
D
E
N
Q
H
P
Y
W
S
T
G
A
M
C
F
L
V
I

(b)

123456789
R
K
D
E
N
Q
H
P
Y
W
S
T
G
A
M
C
F
L
V
I

(c)

(d)

3.0 [half-bit]

Fig. 4. Amino acid propensity at each position in the fragments comprising 9 amino acids of eachdistance class. (a) Propensities for fragments with end-to-end distances of < 10 Å, (b) 10–15 Å,(c) 15–20 Å, and (d) > 20 Å.

(Fig. 4(a)–(d)). The propensity Pijk (in half-bit unit) of amino acid ai at position
j for class k was obtained by the following equation:()
nkj (ai )/Njk
Pijk = 2 log2,n(ai )/N
where nkj (ai ) is the frequency of amino acid ai at position j in the loop fragments ofclass k; Njk is the frequency of any amino acid at position j in the loop fragments ofclass k; n(ai ) is the frequency of amino acid ai at any position in all the fragmentsof any class; and N is the frequency of any amino acid at any position in all thefragments of any class.
The characteristics of amino acid propensity for fragments in each distance classwere clearly observed. In the case of fragments with short end-to-end distances(Fig. 4(a)), disfavor for hydrophobic residues such as Met and Trp and preference
for Asp, Asn, Pro, and Gly were obvious, as described by previous studies [12, 18].
This tendency gradually disappeared as the end-to-end distance of the fragment

September 4, 2009

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

Sequence-Structure Relationships in Protein Loops

9

Table 4. Distributions of the number of Pro residues in all, loop, and extended loop (end-to-end distance of > 20 Å) fragments comprising 9 aminoacids.
Number of Pro residues

0

1

2

3

4

5

All
Loop
Loop (> 20 Å)

0.662
0.484
0.380

0.276
0.381
0.422

0.053
0.111
0.153

0.008
0.021
0.034

0.001
0.003
0.009

0.00010.00030.002

increased (Fig. 4(b,c)), and fragments with end-to-end distances of > 20 Å showedsigniﬁcant preference for Pro (Fig. 4(d)). Table 4 shows the distributions of thenumber of Pro residues in all, loop, and extended loop (end-to-end distance, > 20 Å)fragments comprising 9 amino acids. Among the extended loop fragments, fragmentswith more than 2 Pro residues were not frequently observed, but the average numberof Pro residues per extended loop fragment (0.88) was more than double that per
fragment in the case of all the fragments (0.41).
The extended loop fragments that show a preference for Pro residues correspondto the “Pro-rich extended fragments” proposed by Ikeda et al. [19]. These tendencies
can also be observed for PSSM, and they may explain why SVR can be used to
predict the end-to-end distance for extended fragments. Recently, the polyproline
II-type (PPII) structure has received attention as a type of extended structure ofpolypeptides [9, 24], and a prediction tool for determining the PPII structure on thebasis of amino acid sequences has been developed [27]. According to the descriptionsof PPII residues reported earlier [27], only approximately 10% of fragments with an
end-to-end distance of > 20 Å have at least 5 PPII residues. Our results suggest thatthe sequence-structure relationships in extended loop fragments are not restricted
to PPII structures.
4. Conclusion
In this study, we used a simple machine-learning-based prediction tool to predict
the end-to-end distances of loop fragments comprising 5, 9, and 17 amino acids.
Our prediction was found to be more accurate than random prediction. Extended
loop fragments could be well distinguished from fragments with short end-to-end
distances. Our ﬁndings throw light on the mechanism of protein folding and theprediction of the tertiary structure of proteins without using structural templates.
Most of the local structure prediction tools that were recently proposed are basedon the prediction of a sequence of structural alphabets. The prediction of structuralalphabets is a kind of classiﬁcation prediction and does not consider structuralsimilarity among these alphabets; moreover, this type of prediction provides little
information if the prediction fails. Instead, we directly predicted continuous valuesof the end-to-end distance of fragments as a rough structural property, and we
think this is the reason we could detect signiﬁcant sequence-structure relationships
for fragments with a wide range of end-to-end distances.

September 4, 2009

10

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

S. Nakamura, & K. Shimizu

It is important to note that our prediction tool is rather simple, and hence, thedetected sequence-structure relationships may be lower limit. The use of our toolin combination with other local structure prediction tools such as alpha-, gamma-,
and beta-turn prediction [10, 28, 29], or local structure prediction tools based on
structural alphabets will enhance the ability to detect further relationships between
local sequences and structures.

References[1] Aloy, P., Stark, A., Hadley, C., and Russell, R.B., Predictions without templates: newfolds, secondary structures, and contacts in CASP5, Proteins, 53:436–456, 2003.
[2] Altschul, S.F., Madden, T.L., Schäﬀer, A.A., Zhang, J., Zhang, Z., Miller, W., andLipman, D.J., Gapped BLAST and PSI-BLAST: a new generation of protein databasesearch programs, Nucleic Acids Res., 25(17):3389–3402, 1997.
[3] Anﬁnsen, C.B., Principles that govern the folding of protein chains, Science,
181(4096):223–230, 1973.
[4] Benros, C., de Brevern, A.G., Etchebest, C., and Hazout, S., Assessing a novel approach for predicting local 3D protein structure from sequence, Proteins, 62:865–880,
2006.
[5] Brenner S.E., Koehl, P., and Levitt, M., The ASTRAL compendium for sequence andstructure analysis, Nucleic Acids Res., 28:254–256, 2000.
[6] Bystroﬀ, C. and Baker, D., Prediction of local structure in proteins using a library of
sequence-structure motifs, J. Mol. Biol., 281(3):565–577, 1998.
[7] Bystroﬀ, C., Thorsson, V., and Baker, D., HMMSTR: a hidden Markov model for
local sequence-structure correlations in proteins, J. Mol. Biol., 301(1):173–190, 2000.
[8] Chang, C.C. and Lin, C.J., LIBSVM: a library for support vector machines, 2001.
Software available at http://www.csie.ntu.edu.tw/∼cjlin/libsvm.
[9] De Brevern, A.G., Etchebest, C., Benros, C., and Hazout, S., “Pinning strategy”: anovel approach for predicting the backbone structure in terms of protein blocks fromsequence, J. Biosci., 32(1):51–70, 2007.
[10] Fuchs, P.F.J. and Alix, A.J.P., High accuracy prediction of beta-turns and their types
using propensities and multiple alignments, Proteins, 59:828–839, 2005.
[11] Gront, D. and Kolinski, A., A new approach to prediction of short-range conformational propensities in proteins, Bioinformatics, 21(7):981–987, 2005.
[12] Guruprasad, K. and Rajkumar, S., Beta- and gamma-turns in proteins revisited: a
new set of amino acid turn-type dependent positional preferences and potentials, J.
Biosci., 25(2):143–156, 2000.
[13] Han, K.F. and Baker, D., Recurring local sequence motifs in proteins, J. Mol. Biol.,251(1):176–187, 1995.
[14] Han, K.F. and Baker, D., Global properties of the mapping between local amino acidsequence and local structure in proteins., Proc. Nat’l Acad. Sci. U. S. A., 93(12):5814–
5818, 1996.
[15] Han, K.F., and Bystroﬀ, C., and Baker, D., Three-dimensional structures and contexts
associated with recurrent amino acid sequence patters, Protein Sci., 6:1587–1590,
1997.
[16] Henrick, K. and Thornton, J.M., PQS: a protein quaternary structure ﬁle server,
Trends Biochem. Sci., 23(9):358–361, 1998.
[17] Hunter, C.G. and Subramaniam, S., Protein local structure prediction from sequence,Proteins, 50:572–579, 2003.

September 4, 2009

15:29

WSPC - Proceedings Trim Size: 9.75in x 6.5in

33-Nakamura

Sequence-Structure Relationships in Protein Loops

11[18] Hutchinson, E.G. and Thornton, J.M., A revised set of potentials for beta-turn formation in proteins, Protein Sci., 3:2207–2216, 1994.
[19] Ikeda, K., Tomii, K., Yokomizo, T., Mitomo, D., Maruyama, K., Suzuki, S., and Higo,
J., Protein Sci., 14:1253–1265, 2005.
[20] Kabsch, W. and Sander, C., Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features, Biopolymers, 22(12):2577–2637,
1983.
[21] Kuang, R., Leslie, C.S., and Yang, A.-S., Protein backbone angle prediction withmachine learning approaches, Bioinformatics, 20(10):1612–1621, 2004.
[22] Mönnigmann, M. and Floudas, C.A., Protein loop structure prediction with ﬂexible
stem geometries, Proteins, 61:748–762, 2005.
[23] Murzin, A.G., Brenner, S.E., Hubbard, T., Chothia, C., SCOP: a structural classiﬁcation of proteins database for the investigation of sequences and structures, J. Mol,
Biol., 247:536–540, 1995.
[24] Rath A., Davidson, A.R., and Deber, C.M., The structure of “unstructured” regions
in peptides and proteins: role of the polyproline II helix in protein folding and recognition, Biopolymers, 80:179–185, 2005.
[25] Sander, O., Sommer, I., and Lengauer, T., Local protein structure prediction using
discriminative models, BMC Bioinformatics, 7:14, 2006.
[26] Vapnik, V., The Nature of Statistical Learning Theory, Springer-Verlag, 2000.
[27] Vlasov, P.K., Vlasova, A.V., Tumanyan, V.G., and Esipova, N.G., A tetrapeptidebased method for polyproline II-type secondary structure prediction, Proteins,
61:763–768, 2005.
[28] Wang, Y., Xue, Z.D., and Xu, J., Better prediction of the location of alpha-turns inproteins with support vector machine, Proteins, 65:49–54, 2006.
[29] Wang, Y., Xue, Z.D., Shi, X.H., and Xu, J., Prediction of pi-turns in proteins using
PSI-BLAST proﬁles and secondary structure information, Biochem. Biophys. Res.
Commun., 347(3):574–580, 2006.
[30] Zhong, W., He, J., Harrison, R., Thai, P.C., and Pan, Y., Clustering support vector
machines for protein local structure prediction, Expert Syst. Appl., 32:518–526, 2007.
[31] http://www.predictioncenter.org/casp8/